28 research outputs found
A Novel Approach to Discontinuous Bond Percolation Transition
We introduce a bond percolation procedure on a -dimensional lattice where
two neighbouring sites are connected by channels, each operated by valves
at both ends. Out of a total of , randomly chosen valves are open at
every site. A bond is said to connect two sites if there is at least one
channel between them, which has open valves at both ends. We show analytically
that in all spatial dimensions, this system undergoes a discontinuous
percolation transition in the limit when
crosses a threshold. It must be emphasized
that, in contrast to the ordinary percolation models, here the transition
occurs even in one dimensional systems, albeit discontinuously. We also show
that a special kind of discontinuous percolation occurs only in one dimension
when depends on the system size.Comment: 6 pages, 6 eps figure
Comparison of Modules of Wild Type and Mutant Huntingtin and TP53 Protein Interaction Networks: Implications in Biological Processes and Functions
Disease-causing mutations usually change the interacting partners of mutant
proteins. In this article, we propose that the biological consequences of
mutation are directly related to the alteration of corresponding protein
protein interaction networks (PPIN). Mutation of Huntingtin (HTT) which causes
Huntington's disease (HD) and mutations to TP53 which is associated with
different cancers are studied as two example cases. We construct the PPIN of
wild type and mutant proteins separately and identify the structural modules of
each of the networks. The functional role of these modules are then assessed by
Gene Ontology (GO) enrichment analysis for biological processes (BPs). We find
that a large number of significantly enriched (p<0.0001) GO terms in mutant
PPIN were absent in the wild type PPIN indicating the gain of BPs due to
mutation. Similarly some of the GO terms enriched in wild type PPIN cease to
exist in the modules of mutant PPIN, representing the loss. GO terms common in
modules of mutant and wild type networks indicate both loss and gain of BPs. We
further assign relevant biological function(s) to each module by classifying
the enriched GO terms associated with it. It turns out that most of these
biological functions in HTT networks are already known to be altered in HD and
those of TP53 networks are altered in cancers. We argue that gain of BPs, and
the corresponding biological functions, are due to new interacting partners
acquired by mutant proteins. The methodology we adopt here could be applied to
genetic diseases where mutations alter the ability of the protein to interact
with other proteins.Comment: 35 pages, 10 eps figures, (Supplementary material and Datasets are
available on request
Fixed-Energy Sandpiles Belong Generically to Directed Percolation
Fixed-energy sandpiles with stochastic update rules are known to exhibit a
nonequilibrium phase transition from an active phase into infinitely many
absorbing states. Examples include the conserved Manna model, the conserved
lattice gas, and the conserved threshold transfer process. It is believed that
the transitions in these models belong to an autonomous universality class of
nonequilibrium phase transitions, the so-called Manna class. Contrarily, the
present numerical study of selected (1+1)-dimensional models in this class
suggests that their critical behavior converges to directed percolation after
very long time, questioning the existence of an independent Manna class.Comment: article (4 pages, 9 eps figures) + Supplement (8 pages, 9 eps
figures); Phys. Rev. Lett. 201
Two-dimensional random walk in a bounded domain
In a recent Letter Ciftci and Cakmak [EPL 87, 60003 (2009)] showed that the
two dimensional random walk in a bounded domain, where walkers which cross the
boundary return to a base curve near origin with deterministic rules, can
produce regular patterns. Our numerical calculations suggest that the
cumulative probability distribution function of the returning walkers along the
base curve is a Devil's staircase, which can be explained from the mapping of
these walks to a non-linear stochastic map. The non-trivial probability
distribution function(PDF) is a universal feature of CCRW characterized by the
fractal dimension d=1.75(0) of the PDF bounding curve.Comment: 4 pages, 7 eps figures, revtex
A Novel Approach to Discontinuous Bond Percolation Transition
We introduce a bond percolation procedure on a -dimensional lattice where
two neighbouring sites are connected by channels, each operated by valves
at both ends. Out of a total of , randomly chosen valves are open at
every site. A bond is said to connect two sites if there is at least one
channel between them, which has open valves at both ends. We show analytically
that in all spatial dimensions, this system undergoes a discontinuous
percolation transition in the limit when
crosses a threshold. It must be emphasized
that, in contrast to the ordinary percolation models, here the transition
occurs even in one dimensional systems, albeit discontinuously. We also show
that a special kind of discontinuous percolation occurs only in one dimension
when depends on the system size.Comment: 6 pages, 6 eps figure